Abstract
The stability criterion of a fluid cylinder (density rho((1))) embedded in a different fluid (density rho((2))) is derived and discussed. The model is capillary unstable in the domain 0 < x < 1 as m = 0 where x and m are the axial and transverse wave numbers, while it is stable in all other domains. The densities ratio rho((2)) / rho((1)) decreases the unstable domains but never suppress them. The streaming increases the unstable domains. Gravitationally, in m = 0 mode the model is unstable in the domain 0 < x < 1.0668 as rho((2)) < rho((1)), while as rho((2)) = rho((1)) it is marginally stable but when rho((2)) > rho((1)) the model is purely unstable for all short and long wavelengths. In m not equal 0 modes, the self-gravitating model is neutrally stable as rho((1)) = rho((2)), ordinarily stable as rho((2)) < rho((1)), but is purely unstable as rho((2)) > rho((1)). The streaming destabilizing effect makes the self-gravitating instability worse and shrinks the stable domains. The stability analysis of the model under the combined effect of the capillary and self-gravitating forces is performed analytically and verified numerically. When rho((2)) < rho((1)) the capillary force and the axial flow have destabilizing influences but the ratio of the densities rho((2)) / rho((1)) has a stabilizing effect on the gravitating instability. If rho((1)) = rho((2)), the streaming is destabilizing but the capillary force is strongly stabilizing and could suppress the gravitational instability. When rho((2)) > rho((1)) the capillary force improves the gravitational instability and creates domains of much stability and moreover the instability of the self-gravitating force disappears in several cases of axisymmetric disturbances.